Method for the in situ production of Majorana material superconductor hybrid networks and to a hybrid structure which is produced using the method

ABSTRACT

A method for producing a hybrid structure, the hybrid structure including at least one structured Majorana material and at least one structured superconductive material arranged thereon includes producing, on a substrate, a first mask for structured application of the Majorana material and a further mask for structured growth of the at least one superconductive material, which are aligned relatively to one another, and applying the at least one structured superconductive material to the structured Majorana material with the aid of the further mask. The structured application of the Majorana material and of the at least one superconductive material takes place without interruption in an inert atmosphere.

CROSS REFERENCE TO RELATED APPLICATIONS

This application is a U.S. National Phase Application under 35 U.S.C. §371 of International Application No. PCT/DE2018/000048, filed on Mar. 1,2018, and claims benefit to German Patent Application No. DE 10 2017 002616.5, filed on Mar. 20, 2017. The International Application waspublished in German on Sep. 27, 2018 as WO 2018/171823 under PCT Article21(2).

FIELD

The invention relates to a method for producing a device which makes itpossible to deposit superconductive and Majorana materials in variousgeometries and dimensions and in precise alignment to each other exceptfor a few nanometers, doing so in an inert atmosphere and preferably inan ultra-high vacuum and to preserve them with a passivating protectivelayer. Complex networks of said materials can be fabricated with thedevice. These networks include as the smallest subunit a hybridstructure, such as a topological Josephson contact but in a furtherembodiment may represent up to a plurality of topological quantum bits.The method preserves the surface properties of the Majorana material anda high interface quality between the Majorana material and thesuperconductor.

BACKGROUND

In order to represent bits, distinguishable physical states must bepresent, which are defined in traditional transistor technology by twodistinguishable voltage values. In the case of a quantum computer, thesestates are represented by distinguishable quantum-mechanical states.Such a quantum computer is characterized by a large number, in extremecases by an arbitrarily large number, of distinguishable states whichrepresent the bits, the so-called quantum bits (qubits). For thisreason, certain calculations can be solved much more quickly andefficiently on a quantum computer. Thus, Google showed in January 2016that they could solve a problem approximately 100,000,000 times fasterwith their D-Wave quantum annealer than with a traditional computer. Aquantum annealer is a special type of quantum computer, which canhowever only be used for optimization problems. The total computingpower made possible by quantum mechanics only becomes apparent in aso-called universal quantum computer. The main problem of universalquantum computers is that the very sensitive and short-lived quantumstates are not stable and simply reading these states can result in achange of state. The errors resulting therefrom must be correctedimmediately after each computation step. This error correction is thereason why development of a universal quantum computer is onlyproceeding slowly and why during the last 30 years it has not beenpossible to realize a universal quantum computer with a two-digit numberof qubits. In the field of error-corrected quantum computing, Googlealso reached a milestone at the beginning of 2016 and built to date themost powerful error-corrected universal quantum computer. Unlike the1000 qubits of the D-Wave 2X quantum annealer, only 8 qubits areimplemented in this case. IBM has also developed a first universalquantum computer with five qubits, which has even been made available tothe public within the framework of Quantum Experience since May 2016.However, at least 50 qubits are required in order to performcomputations that currently cannot be solved even by modernsupercomputers [1].

In order to achieve the goal of a quantum computer with 50 qubits asquickly as possible, scientific and industrial institutions are focusingon a relatively young sector of quantum computing, so-called topologicalquantum computing. The fact that in theory no error correction isrequired for this type of quantum computer, and only a very small degreeof error correction in practice, makes this approach particularlypromising and brings the arrival of a 50-qubit machine into the nearfuture.

As in conventional (non-topological) quantum computers, quantum objectsor particles (objects, particles or quasiparticles that follow the lawsof quantum mechanics) must also be actively integrated into thecalculation process in topological quantum computers and to this end bepositioned on a chip, separately controlled, manipulated and read out.The quantum-mechanical quasiparticle, on the basis of which thetopological quantum computer computes, is the so-called bound Majoranazero mode (MZM). MZMs are 0-dimensional quasiparticle excitations thatpromise new concepts for more error-tolerant quantum computing due totheir non-Abelian commutation relations.

MZMs can arise when connecting so-called Majorana materials tosuperconductive materials. In this document all materials in whichMajorana zero modes are produced as soon as these materials are broughtinto contact with a superconductor and the fields (E field and B field)necessary for generating the MZMs are applied are referred to asMajorana materials. Majorana materials are, for example, Diracmaterials, which in turn can be classified into topological insulatorsand Weyl metals by way of example, as well as “half-metals” which arenot to be confused with semimetals, as well as III-V semiconductornanowires. Majorana materials necessarily have fermionic states that donot have any spin degree of freedom (in the English language and in thefurther course of this document, these states are called “spinlessfermions”). In a subset of Majorana materials, so-called topologicalinsulators (TIs), the spin-path interaction in the solid, for example,results in the direction of spin for fermionic states at the surface ofthe TIs being directly coupled to the k vector in the momentum space. Ifsuperconduction is induced in such a spinless-fermions system, MZMs willarise under suitable circumstances (spatial geometry of the Majoranamaterial, E and B fields).

Signatures of MZMs were demonstrated in InAs nanowires for the firsttime in 2012 by the group around Leo Kouwenhoven [3] and subsequentlydemonstrated in other material systems as well. Majorana zero modes inprinciple always arise in pairs, and in the case of 1D structures, thetwo modes appear locally separately at the two ends of the 1D structurein the form of 0D excitations. Together, the two Majoranas form afermionic state. This state can either be occupied by an electron orunoccupied. In order to find out whether or not an electron is presentin the two Majoranas, the two Majoranas must be moved towards eachother. As soon as they “touch” or their wave functions overlap, theyfuse into an electron or they are annihilated and no electron isproduced.

The two states of “no electron” and “an electron” form the twoeigenstates of the Majorana pair, or of the Majorana qubit, analogous tothe eigenstates of “spin-up” and “spin-down” of a conventional spinqubit.

A fundamental difference from conventional qubits is that botheigenstates of Majorana qubits have the same energy, i.e. aredegenerate. In conventional qubits, there is always an excited state anda ground state. If the qubit remains in the excited state for too long,it relaxes to the ground state and the information is lost. This cannothappen with the Majorana qubit. These and other properties result inMajorana qubits theoretically not requiring any error correction [2].This fact significantly reduces the technological effort for a 50-qubitmachine and makes the concept of topological quantum computing soattractive.

In order to do quantum computing with Majoranas, that is, to change thestate of one or more qubits, these 0-dimensional objects must bearranged in a two-dimensional plane. It is also important that they canbe moved around each other and towards each other. In particular, thequantum-mechanical state of a 2-Majorana system is changed by rotatingthe two Majoranas around each other. If a system is initialized in thestate |0>(=no electron) and the two Majoranas are subsequently rotatedaround each other by 360°, the state will be changed to |1>. If the twoMajoranas are now allowed to fuse together, an electron will be measured100% of the time and an unoccupied state 0% of the time. The probabilityof measuring an electron is 50% in the case of a 180° rotation aroundeach other, but only 25% in the case of a 90° rotation, and so on.

In principle, a topological quantum computer thus consists of a certainnumber of Majoranas which are arranged in a plane and which can bepurposefully rotated around each other (or braided). The possibilitiesof the braiding operations and thus the performance of the quantumcomputer increase with the number of Majoranas. The challenge is toarrange (quasi-) 1D structures or nanowires in such a way that theMajorana modes can be moved according to requirements.

There are various approaches to generating Majorana modes and producingthe first networks based thereon. The first signatures of Majorana modeswere demonstrated in 2012 in InAs nanowires [2]. Based on these andsimilar concepts, intensive research is being conducted with the goal ofbuilding the first Majorana qubits soon. For example, US 2016/0035470 A1discloses a magnetic topological nanowire structure comprising asuperconductor and a quasi-1D magnetic nanowire. The quasi-1D magneticnanowire is coupled to or embedded in the superconductor in order toproduce a self-contained interaction resulting in a spatially separatedpair of Majorana fermions.

The approach of constructing Majorana qubits from individualsemiconductor nanowires has two decisive disadvantages. On the one hand,a relatively strong magnetic field is required in these nanowires forthe topological phase to be reached. Only in this phase can Majoranamodes be generated [4]. Furthermore, in order to build qubits fromsemiconductor nanowires, the individual nanowires must be alignedrelatively to one another with nanometer precision. Whether working withindividual nanowires or with networks of grown nanowires, the scaling ofthis approach requires an enormous amount of effort.

Some Majorana materials, such as topological insulators, inherently havethe required topological properties. In this case, only the chemicalpotential must lie within the intrinsic bulk-energy gap for Majoranaphysics to be possible in practice. In 2016, signatures of Majoranamodes in topological insulators were found for the first time in twoindependent experiments. If the spatial dimensions of the topologicalinsulator are to be limited such that an energy gap results within thedispersion of the surface states, it is also necessary to apply amagnetic field/magnetic flux through the structure. This magnetic fieldis very small relative to the necessary magnetic fields for Zeemansplitting of the Rashba bands in InAs nanowires. The characteristic sizehere is half of a magnetic flux quantum, which, in the dimensions usedin the text below, corresponds to a magnetic field of no more than 150mT [5, 6].

In addition to the decisive advantage that no magnetic field is requiredfor generating the topological phase in these materials, there is afurther advantage:

Certain topological insulators, such as (Bi_((1-x))Sb_(x))₂Te₃ where0≤x≤1, grow selectively [e.g., on Si (111) with respect to SiO₂ orSi₃N₄] [7]. Prior to their growth, preliminary structures can be definedwithout much effort in a very extensive and complex manner by optical orelectron beam lithography. This technique makes it possible to realizecomplex geometries in a very short time.

In the case of topological insulators, the spinless fermions in Majoranamaterials are located at the surface of the solid. If the surface of thetopological insulator is exposed to the ambient air outside an inertenvironment, the oxidation which then takes place will cause the Diracstates—as the system of spinless fermions in the surface of atopological insulator is termed—and thus surface transportation to bedisturbed. It was found that a passivation layer for protecting thetopological insulator from oxidation or degradation of the surfacestates can still be arranged on a topological insulator in the inertatmosphere, in particular in the ultrahigh vacuum (p≤1×10⁻⁷ mbar,preferably p≤1×10⁻⁸ mbar). The surface states can thereby be retained. Athin layer of aluminum of approximately 2 nm layer thickness, which cancompletely oxidize and thereby protects the topological insulator, can,for example, be used as a passivation layer. Alternatively, Te, Se andother insulating layers are also already used as passivation layers. Itis therefore important to seal the entire surface of the topologicalinsulator before it is outwardly transferred from the inert atmosphereand where applicable the ultrahigh vacuum and to thus preserve thesurface states for Majorana physics. An inert atmosphere refers to anatmosphere which, in a manner adapted to the (Majorana) material,prevents any (chemical) reaction of the atoms and molecules in theatmosphere with the surface of the material.

In order for Majorana modes to arise, a superconductor must also bepresent as a second prerequisite in addition to the topological phase.Two superconductive contacts, which are separated by a small distance(5-150 nm) and which are connected by a material which is inherently notsuperconductive but becomes superconductive in the region between thecontacts at low temperatures as a result of the presence of thesuperconductors, are referred to as a Josephson junction. If the“inherently non-superconductive” material is a Majorana material, theJosephson junction is called a topological Josephson junction. TheJosephson junction is one of the simplest hybrid components, consistingof superconductor and Majorana material, and the basic component formany more complex components.

It is known from the prior art to apply superconductive Josephsoncontacts ex situ. For this purpose, the Majorana material, or morespecifically the topological insulator, may first be deposited via avacuum-based coating method or thin-film technology (physical vapordeposition (PVD), chemical vapor deposition (CVD), advantageouslymolecular beam epitaxy (MBE)). The superconductive contacts can then besubsequently defined by electron beam lithography (EBL) in a resistsuitable for this purpose and can afterwards be vapor-deposited orsputter-deposited in another system. If the topological insulator hasbeen sealed with a capping (passivation), this capping must be removedimmediately prior to deposition of the superconductor, since thesuperconductor must be in direct contact with the Majorana material. Insuch a procedure, the risk routinely exists that the surface of theMajorana material will already oxidize or react with the ambient airbefore the superconductive material is applied. This leads, for example,to defects and to amorphizing surface regions, i.e. to an interfacebetween the Majorana material and the superconductor encumbered withimperfections and unevennesses. These have a disadvantageous effect astunnel barriers. Such interfaces are generally not suitable for thepractice of Majorana physics.

For other material systems, such as InAs, it is furthermore known toapply in situ a homogeneous layer of superconductive material, inparticular aluminum, to thin films [8]. The superconductive materialsare subsequently chemically and/or physically structured. This is doneby removing subregions of the superconductive layer.

By applying the superconductive materials without leaving the inertatmosphere and in particular the ultrahigh vacuum, an interface of veryhigh quality can be created between the Majorana material (or thetopological insulator) and the superconductor. Disadvantageously, theremoval of subregions of the superconductive layer also always leads toa change in or destruction of the surface of the underlying material.This leads to a chemical change in the surface, in particular whentopological insulators are used.

A nanometer-precise removal of a superconductive layer arranged on aMajorana material and a subsequent local oxidation of this region isgenerally not possible because of the surface properties of thesuperconductor. In the case of aluminum, the surface of the aluminumwould regularly also be too rough.

Known from the prior art is so-called stencil lithography. Thistechnology enables subregions of a substrate or thin film to be providedwith a second structured layer (in situ) by means of a shadow mask (hardmask) [9, 10]. The use of hard masks makes it possible to structure asecond, for example a superconductive, layer within the inert atmosphereand advantageously in the ultrahigh vacuum. Structuring is carried outin this case in systems with partially directed material flow byreproducing the structures defined on the hard mask.

SUMMARY

In an embodiment, the present invention provides a method for producinga hybrid structure, the hybrid structure including at least onestructured Majorana material and at least one structured superconductivematerial arranged thereon. The method includes producing, on asubstrate, a first mask for structured application of the Majoranamaterial and a further mask for structured growth of the at least onesuperconductive material, which are aligned relatively to one another,and applying the at least one structured superconductive material to thestructured Majorana material with the aid of the further mask. Thestructured application of the Majorana material and of the at least onesuperconductive material takes place without interruption in an inertatmosphere.

BRIEF DESCRIPTION OF THE DRAWINGS

The present invention will be described in even greater detail belowbased on the exemplary figures. The invention is not limited to theexemplary embodiments. All features described and/or illustrated hereincan be used alone or combined in different combinations in embodimentsof the invention. The features and advantages of various embodiments ofthe present invention will become apparent by reading the followingdetailed description with reference to the attached drawings whichillustrate the following:

FIG. 1 illustrates a process for preparing a substrate for a structureddeposition of a Majorana material by producing a first functional maskon the substrate according to an embodiment of the invention;

FIG. 2 illustrates a process for producing a shadow mask close to asurface for a defined application of at least one superconductivematerial to a substrate according to an embodiment of the invention;

FIG. 3 illustrates a process for directed and structured application offunctional layers according to an embodiment of the invention;

FIG. 4 illustrates a process for directed and structured application offunctional layers according to an embodiment of the invention;

FIG. 5 illustrates the production, after outward transfer, of aJosephson junction according to an embodiment of the invention;

FIG. 6 illustrates the production, after outward transfer, of aJosephson junction according to an embodiment of the invention;

FIG. 7 illustrates plan views of Josephson junctions according to anembodiment of the invention; and

FIG. 8 illustrates plan views of Josephson junctions according to anembodiment of the invention.

DETAILED DESCRIPTION

Embodiments of the invention provide methods by way of whichMajorana-material superconductor structures, also referred to below ashybrid structures, comprising at least one structured Majorana materialand at least one superconductive material arranged thereon in astructured manner, can in a few process steps be generated as thesmallest unit of a Majorana-material superconductor hybrid network. Onthe one hand, the methods provide a high quality of the surfaces andinterfaces and additionally provide passivation of the structuredMajorana material. In particular, the methods enable preservation of thegenerated surface states, in particular for Majorana physics.

Furthermore, the method should make it possible for the structuredMajorana material and the superconductive material to be alignedrelatively to one another with high accuracy, and for a high scalabilityto be ensured.

Furthermore, embodiments of the invention provide high-quality hybridstructures, with which networks of any complexity can be constructedfrom Majorana-material superconductors, by means of the aforementionedmethods.

According to the invention, methods are provided for producing aMajorana-material superconductor structure, hereinafter called a hybridstructure for short, comprising at least one structured Majoranamaterial, at least one structured superconductive material arrangedthereon, and a passivation layer arranged on the free surface(s) of thestructured Majorana material.

According to embodiments of the invention, hybrid structures comprisingat least one structured Majorana material, in particular comprising atleast one structured Majorana material in the form of a laterally grown(quasi-) 1D nanowire or a laterally grown (quasi-) 1D nanostructure, atleast one structured superconductive material arranged thereon, and apassivation layer arranged on the free surface of the structuredMajorana material, are provided.

The invention provides methods in which a Majorana-materialsuperconductor structure—a hybrid structure for short—can be producedwith the aid of a mask close to the surface. This hybrid structurecomprises at least one structured Majorana material which is definedwithin the scope of this invention as a laterally grown (quasi-) 1Dnanowire or a laterally grown (quasi-) 1D nanostructure, wherein thelatter, for example, can take the form of a structured topological thinfilm. In addition to the structured Majorana material, the hybridstructure has at least one structured superconductive material arrangedon this structured Majorana material and a passivation layer arranged onthe free surfaces of the structured Majorana material, said material notbeing contacted by the superconductive material.

In the structures according to the invention, a particular quality ofthe interface between, for example, a topological insulator and asuperconductive metal is ensured by in-situ and preferably by epitaxialgrowth of both layers.

Furthermore, with the methods according to the invention, a protectivepassivation layer can also be produced directly during production overexposed regions of the structured Majorana material, whichadvantageously leads to the surface states thereof being neitherdestroyed nor changed. Surface states in topological insulators are alsocalled Dirac states.

In the methods according to the invention, in addition to a mask knownfrom the prior art for structured application of at least onesuperconductive material on a Majorana material (shadow mask, hard mask,stencil mask), a further mask which serves for depositing the Majoranamaterial on a substrate in a defined geometry is advantageouslypreviously produced directly on the substrate (mask for producing apreliminary structure, “selective area”). The formation of two masks onthe substrate in the production of the hybrid structure subsequentlyadvantageously leads to both the deposited structured Majorana materialand the subsequently at least one superconductive structure being ableto preferably be precisely aligned relatively to each other even duringtheir production. Since the process steps are carried out throughout inan inert atmosphere and preferably in the ultrahigh vacuum, a very highquality of the interfaces of the hybrid structure can additionally beensured according to the invention.

By the methods according to the invention, laterally grownheterostructures of superconductive materials and Majorana materials canadvantageously be produced with high quality and precise alignment.Various geometries and dimensions allow the structured definition offunctional devices, starting with topological Josephson junctions up tocomplex networks for applications in scalable topological qubits as wellas topological quantum registers.

According to the invention, both the structured Majorana material andthe superconductive material can be laterally grown. In the methodsaccording to the invention, both the structured Majorana material andthe superconductive material are structured and applied relatively toeach other without the need to carry out this processing after thedeposition. In comparison to previously known methods of in-situstructuring, the methods according to the invention offer particularadvantages in the abruptness of the interfaces and the possibledimensioning of the individual functional layers.

Such high-quality hybrid structures produced according to the inventioncan preferably be used in topological Josephson contacts but also incomplex components, such as topological SQUIDs (abbreviation forsuperconductive quantum interference devices), topological qubits(abbreviation for quantum bits) and topological quantum registers, whichserve as the smallest unit for the well-defined junction of atopological material and a superconductor.

For the mentioned applications of such hybrid structures in Majoranaphysics and the topological quantum computing based thereon, it isnecessary for the components or interfaces to be produced to be of highquality, as they provide the structures according to the invention.

A Josephson contact, which, for example, comprises such structuresaccording to the invention, refers to two superconductive materialswhich are separated from each other by a thin, non-superconductiveregion. In the following, the term “weak link” refers to the regionwhich separates the two superconductors from each other in the Josephsoncontact and which is not superconductive by definition.

The invention is described in more detail below with reference to anexample of a topological Josephson contact as an example of a hybridstructure according to the invention, without being limited thereto. Thetopological Josephson contact comprises two superconductive materialsarranged laterally to one another and a structured Majorana materialcharacterizing the non-superconductive region (weak link).

It is known from the prior art that a weak link as an intermediateregion between two superconductors comprising a topological material canlikewise be superconductive if the distance between the superconductorsis sufficiently short. Such a distance is sufficiently short if it isless than the coherence length of the paired electron states in thetopological material. In the case of aluminum as superconductivematerial, the coherence length is known to be 100-400 nm, depending onthe quality of the crystalline material and the boundary layer betweensuperconductor and topological material. When using niobium, thischaracteristic value of the coherence length is somewhat reduced due tothe higher transition temperature and lies in a range between 50-250 nm.

In the case of a Josephson contact, quality assurance means that on theone hand a good transportation is ensured in the region of the weaklink, for which purpose an in-situ covering (capping) is necessary, andthat on the other hand the contact has a clean and sharp interfacebetween the superconductors and the structured Majorana material. Thiscan be achieved in particular by in-situ and preferably by epitaxialgrowth of both layers. Both the structured and relatively aligned growthof the structured Majorana material, the in-situ capping, and thein-situ application of the preferably epitaxial, superconductivecontacts are made possible by the method according to the inventionwithout departing from an inert atmosphere and/or ultrahigh vacuum inthe process.

In order to produce such a hybrid structure, the invention provides forusing, in addition to an already known stencil mask (shadow mask), afurther mask by means of which the geometry of the structured Majoranamaterial can be defined and which is likewise firmly connected to thesubstrate.

A method according to the invention for producing hybrid structures isspecified below with reference to an example of a Josephson contactusing a topological insulator and superconductive metals, without beinglimited to this specific embodiment.

The individual steps of a method according to the invention can befollowed on the basis of FIGS. 1 to 6 with reference to the example ofthe production of a Josephson junction (Josephson contact) as a hybridstructure according to the invention. The materials or layer detailsmentioned by way of example in the process steps below are expressly notto be understood as limiting. A person skilled in the art can easily seewhich details relate specifically to the Josephson junction and wouldhave to be modified accordingly in the production of other hybridstructures.

The production of a Josephson contact described here by way of exampleis not to be understood as limiting but at the same time serves as thesmallest unit of a topological qubit as an illustration of the exemplaryembodiments listed thereafter. The letters given to the process stepsfor producing an individual topological Josephson contact correspond tothose in FIGS. 1 to 6. Further exemplary embodiments for producing morecomplex devices based on such individual Josephson contacts can be seenin FIGS. 7 to 8.

A method according to the invention can be divided into threesubprocesses in all.

-   -   Subprocess I: Preparing the substrate for a structured        deposition of the Majorana material (process step (I) “Selective        area”) by producing a first functional mask on the substrate.    -   Subprocess II: Producing a shadow mask (stencil mask) close to        the surface for the defined application of at least one        superconductive material (process step (II) “Stencil mask”) to        the substrate as well.    -   Subprocess III: A method during deposition within a vacuum        chamber for the directed and structured application of the        functional layers (process step (III) “Coating method”).

In order to distinguish between various possibilities of depositingfunctional structures in a structured manner with the aid of thegenerated mask, the third subprocess also comprises two differentvariations.

Subprocess I: “Selective Area”

I.A A first additional layer (2) is applied areally and under vacuum,preferably in the ultrahigh vacuum, to a cleaned substrate (1). Thesubstrate may be, for example, a silicon wafer of any type or a siliconwafer portion. A cleaned substrate is understood to be one which hasbeen treated with a standard substrate-typical method known to theperson skilled in the art for removing contaminations on the substratesurface. In this way, a substrate surface is provided which has onlysubstrate-inherent connections.

The material of the substrate must be suitable for the growth of atopological insulator thereon. A material which can be selectivelyetched with respect to the substrate and the second layer (3) canpreferably be used for the first layer (2). Suitable for this purposeis, for example, silicon dioxide (SiO₂), wherein the latter shouldpreferably be of high quality and able to be produced by way of examplein a method for thermal conversion of the silicon surface.Advantageously, this SiO₂ has very good etching selectivity incomparison to the silicon of the substrate (1) and of the secondadditional layer (3).

The SiO₂ layer can, for example, be removed isotropically byhydrofluoric acid, wherein an atomically flat surface suitable forgrowth is produced on the substrate. Advantageously, the SiO₂ layer alsohas dielectric properties, whereby leakage currents can be suppressed.From the prior art is known that when stoichiometric silicon nitride(Si₃N₄) is used as second additional layer (3), a thin SiO₂ layer 1 to10 nm thick effectively reduces or prevents tensions which the Si₃N₄ canexert on the silicon surface. Tensions in the silicon substrate can havea negative effect on the covering of the substrate by the firstfunctional layer (6).

The selected layer thickness of the first layer (2) should compensatepossible tensions on the substrate. A possible range of 1 to 20 nm,preferably a range of 1 to 5 nm, is selected as the layer thickness forthe first layer (2).

I.B A second additional layer (3) is applied areally and under vacuum tothe first additional layer (2). Said layer (3) is characterized in thatit can be removed selectively with respect to the first additional layer(2). In the exemplary embodiment given, the second layer should beHF-resistant and in particular low-tension. In the foregoing example,stoichiometric silicon nitride (Si₃N₄) having a low density of parasitichydrogen compounds is used by way of example. A suitable method in thiscase is the deposition of the nitride from the gas phase under lowpressure (low-pressure chemical vapor deposition, LP-CVD). A transparentSi₃N₄ layer can advantageously be used as a mask in wet-chemical or dryetching methods. The second additional layer (3) is used to definesubregions on which the topological insulator is not depositedselectively with respect to the silicon substrate during growth.

The surface of the second layer (3) advantageously ends at the surfaceof the first functional layer (6) in process step III.I. The layerthickness should therefore be selected in the range of 0.2 to 250 nm,preferably in the range of 5 to 100 nm.

I.C After application of the second additional layer (3), this layer isstructured, advantageously via electron beam lithography (EBL) using asuitable lacquer or resist. After the development of the lacquer, thestructures defined in the resist are transferred into the secondadditional layer (3) by means of a suitable etching method. The secondadditional layer (3) is in this respect partly removed in a selectiveand structured manner with respect to the first additional layer (2).

The desired structures in the second additional layer (3) canadvantageously be precisely produced by reactive ion etching (RIE), inparticular in an Si₃N₄ layer. In particular, anisotropic structures areproduced by this directed etching method.

Suitable in the example presented here is reactive ion etching using, byway of example, fluoroform and pure oxygen as reactive gas constituents.Alternatives would be, for example, the wet-chemical removal of thesilicon nitride by phosphoric acid or physical removal of the siliconnitride with the aid of accelerated ions, e.g. in an ion beam system(ion beam etching, IBE).

In the method presented here for structuring the second layer (3), thintrenches having a width of 10-10 000 nm, preferably of 30-200 nm, are,for example, defined in the second layer (3). The length of the trenchesproduced preferably varies between 100 nm and 100 μm, preferably between3 and 10 μm. The trenches may also be defined in ring or rectangularstructures.

Via method steps A to C, a first functional mask is thus formed, withthe aid of which, according to the invention and advantageously, adefined geometry of the structured Majorana material is made possible.

I.D The exposed subregions of the first additional layer (2) areselectively removed with respect to the second additional layer (3) andthe substrate (1). A process which does not chemically convert thesubstrate (1) and/or damage the substrate surface is preferably usedhere. By way of example, dilute hydrofluoric acid, which selectivelyetches the silicon dioxide and uncovers the surface of the siliconsubstrate unchanged, is used.

The isotropic etching behavior of the silicon dioxide in the dilutehydrofluoric acid forms an etching profile close to that shown in FIG.1, process step D.

Subprocess II: “Stencil Mask”

II.E In a first step, a third additional layer (4) is deposited areallyand under vacuum on the structures produced in subprocess I. Said layershould be selectively removable with respect to the substrate (1) andthe first (2) and second (3) additional layers. By way of example,silicon dioxide with reduced quality with respect to the first silicondioxide layer (2) is used here, as soon as it can be deposited from thegas phase at low pressure (low-pressure chemical vapor deposition,LP-CVD). This second layer of silicon dioxide (4) is etchedsignificantly faster in dilute hydrofluoric acid so that this layer canbe removed selectively with respect to the first silicon dioxide layer(2) through the selection of the etching time.

The selected layer thickness of the third additional layer (4) definesthe distance of the mask (shadow mask) that is close to the surface fromthe substrate surface (1). Up to four functional layers are deposited onthe substrate surface in subprocess III. A range of 5 to 500 nm,preferably a range of 10 to 150 nm, is therefore selected as the layerthickness for the third additional layer (4).

II.F A fourth additional layer (5) is applied areally and under vacuumto the third additional layer (4). Said fourth additional layer shouldbe selectively removable with respect to the third additional layer (4).When using silicon nitride again, the methods mentioned in process stepI.C can be used.

II.G The fourth additional layer (5) is partially removed selectivelywith respect to the third additional layer (4). The structures to beproduced vary depending on the desired device. Various embodiments ofthe structures are described by way of example in the section with theexemplary embodiments. The structures here include both large areas andsmall, narrow junctions, both of which are aligned relatively to theproduced structures in the first additional layer (2). Said junctions,which ultimately define Josephson contacts, have at least the width ofthe structures in the first additional layer (2) previously produced inprocess step I.C and a lateral distance from one another of 10-500 nm,preferably 10-200 nm. This narrow region is referred to hereinafter asthe nanobridge.

II.H The third additional layer (4) is at least partially removedselectively with respect to the substrate (1) as well as the first (2),second (3) and fourth additional layers (5). In the process, the regionsexposed in step II.G are removed. It is necessary for a method accordingto the invention that the third additional layer (4) be removedisotropically in all directions. As a result, any material of the thirdadditional layer (4) beneath the nanobridges defined in step II.G isremoved. In addition, the structures defined in submethod I arepartially exposed. The nanobridges are partially freely suspended abovethe substrate (1) from this point in time on.

In this respect, a second functional mask, which is frequently alsocalled a shadow mask, is formed via method steps D to F.

In this respect, the two subprocesses I and II serve for preparing theactual deposition or generation of the functional layers of the hybridstructures on the substrate.

The subsequent process steps I to K are carried out successively in aninert atmosphere without interrupting the vacuum, and in particular theultrahigh vacuum (p≤1×10⁻⁷ mbar, preferably p≤1×10⁻⁸ mbar). Pure N₂ gasis regarded as an inert atmosphere, for example.

Subprocess III: “Coating Method” Variant A

III.I The sample with the nanobridges and the partially exposed areas ofthe substrate (1) is transferred into a vacuum chamber, for example intothat of a molecular beam epitaxy system, for the deposition of thefunctional layers/structures. However, this method step can also takeplace in other coating installations in which the growth is carried outin a partially directed manner. The growth of III/V nanowires in achemical vapor deposition (CVD) system can be mentioned here by way ofexample. The first functional layer (6) is deposited. This layer mustgrow selectively on the exposed substrate surface (1), while it isnecessary that no material be deposited on the exposed surfaces of theadditional layers (2, 3) and advantageous that no material be depositedon the surfaces of the additional layers (4, 5). The first functionallayer (6) comprises Majorana materials.

Topological insulators of the form (Bi_(x)Sb_(1-x))₂(Te_(y)Se_(1-y))₃,where 0≤x≤1 and 0≤y≤1, for example, grow on a silicon (111) surfaceselectively with respect to silicon dioxide (2, 4) and silicon nitride(3, 5) surfaces.

This deposition is carried out with a substrate rotation of 1-500 min⁻¹,which guarantees that the topological insulator also grows on theexposed subregions beneath the nanobridges.

The first functional mask produced by method steps A to C defines thestructure of the Majorana material.

The layer thickness is adjusted in particular in such a way that thesurface of the topological thin film (6) preferably ends at the exposedsurface of the second layer (3).

III.J A second functional layer (7) which is capable of forming a nativeoxidation layer, for example aluminum or niobium or tungsten, titanium,hafnium or platinum, is also applied in a surface-covering manner withsubstrate rotation. Preferably, a superconductive metal is used, forexample, aluminum or niobium. Due to the substrate rotation, this layeris also deposited beneath the nanobridges.

In the embodiment described here, the layer thickness of the secondfunctional layer (7) must not exceed the thickness of the native oxideof the respectively selected material in order to be able to form apassivation layer for the topological insulator in subsequent steps.

In one embodiment of the method, a thin film comprising aluminum isapplied, since a passivation layer can advantageously be specificallyformed in aluminum. For example, the thin film comprising aluminum canbe applied with a layer thickness of at most 3 nm, because this layerthickness ensures that the aluminum layer as the second functional layer(7) completely oxidizes in a subsequent oxidation as soon as it comesinto contact with air.

III.K A third functional layer (8) comprising a superconductivematerial, for example aluminum or niobium, is applied without substraterotation in a structured manner to subregions of the second functionallayer (7). The nanobridges defined in the fourth additional layer (5)partially shadow the atomic/molecular flow. Due to this partialshadowing of the atomic/molecular flow, the second functional layer (7)is not coated completely areally but only in subregions.

The layer thickness of the now deposited material (8) should on the onehand be at least the critical thickness for obtaining thesuperconductive properties of the material but should on the other handnot fall below the thickness of a native oxide formed in a subsequentstep of the material used.

In addition, the layer thickness of the third functional layer (8)should not exceed the distance between the surface of the secondfunctional layer (7) and the lower edge of the fourth additional layer(5), since otherwise an undesired contact of the generated hybridstructure and the shadow mask cannot be ruled out.

The layer thickness of the deposited subregions (8) regularly amounts to5-500 nm, depending on the chosen layer thickness of the firstadditional layer (2). The layer thickness should preferably be selectedbetween 30 and 100 nm in order to ensure the superconductive propertiesof most superconductive metals, wherein the subsequent formation of theoxide layer should also be taken into account.

The material of the second functional layer (7) can be selectedidentically to the material of the third functional layer (8), i.e. asuperconductive material. However, the two materials can also beselected differently, since superconduction is not absolutely necessaryfor the function of the second functional layer, but the formation of anative oxide layer as passivation layer is paramount. When selecting anon-superconductive material as an interdiffusion barrier, it should betaken into account that this barrier is chosen to be thin enough for theproximity-induced superconduction to be ensured via the defined weaklink.

In a method according to the invention, it is therefore, for example,advantageous to select titanium as the second functional layer (7) sinceit can serve as an interdiffusion barrier between the first functionallayer (6) and the third functional layer (8), but to select anothersuperconductive metal, for example aluminum or niobium, as the thirdfunctional layer (8) since these metals have particularly advantageoussuperconductive properties with respect to titanium.

Submethod III: “Coating Method” Variant B

III.I This method step corresponds to that of variant A.

III.J′ A second functional layer (9) comprising superconductivematerial, for example aluminum or niobium, is applied without substraterotation to subregions of the first functional layer (structuredMajorana material) (6). The nanobridges defined in the fourth additionallayer (5) partially shadow the atomic/molecular flow. Similarly toIII.K, due to this partial shadowing of the atomic/molecular flow, thestructured Majorana material (6) is coated with the superconductivematerial of the second functional layer (9) only in subregions in a notcompletely areal but structured manner.

In an alternative embodiment, the second functional layer (9) can alsobe applied as a layer system consisting of a thin interdiffusion barrierand a thick superconductive layer. A metal or a superconductor canpreferably be selected as the material for the interdiffusion barrier.For the layer thickness of the superconductive layer, the criticalthickness for obtaining the superconductivity must again be taken intoaccount. Thin layers of platinum, tungsten or titanium are, for example,known as an interdiffusion barrier from the literature. When selecting anon-superconductive material as an interdiffusion barrier, it should betaken into account that this barrier is chosen to be thin enough forproximity-induced superconduction to be ensured via the defined weaklink.

The thickness of the deposited material for the second functional layer(9) should be at least the critical thickness for obtaining thesuperconductive properties of the material, wherein the layer thicknessof the native oxide must additionally be taken into account. This formswhen after deposition the material used comes into contact withatmospheric oxygen or oxygen in any other form.

The thickness of the subregions of the second functional layer (9) istherefore advantageously between 50 and 100 nm, wherein the thickness ofthe material should not exceed the distance between the surface of thefirst functional layer (6) and the fourth additional layer (5).

III.K′ A third functional layer (10) comprising an electricallyinsulating material is applied in a surface-covering manner to thesecond functional layer (9)/the layer system, as well as to the exposedregions of the first functional layer (6). This definition includesoxidizing metals as mentioned in process step III.J.

In this embodiment of submethod III, however, other materials canadvantageously also be used to protect the surface and the surfacestates of the structured Majorana material in the subregions produced inprocess step III.J′. The materials used should have a sufficiently highband gap such that no cohesive tunneling of charge carriers in theselected material can occur in the technically relevant temperaturerange, taking into account the actual electron temperature. Thetechnically relevant range is defined by the characteristic criticaltemperature of the superconductor used.

This third functional layer (10) preferably reacts/interdiffuses neitherwith the first functional layer (6) nor with the second functional layer(9). Silicon nitride may be used as the third functional layer (10), forexample.

Furthermore, inert metal oxide compounds, such as Al_(x)O_(y),Nb_(x)O_(y), Ti_(x)O_(y), where 0≤x, y≤1, or even inert metal compoundswith other group VI elements, such as sulfur, tellurium or selenium, arealso suitable. Layers of pure tellurium or selenium can likewise bedeposited as temporary protection of the topological surface states.

By methods according to the invention, laterally grown heterostructuresof structured superconductive materials and structured Majorana materialcan advantageously be produced with high quality and precise alignment.This is important, for example, for the characterization of thesuperconductive properties of topological materials but ultimately alsofor applications in scalable topological qubits as well as quantumregisters.

All ex-situ steps used in the prior art can advantageously be bypassedin a clean room by the methods according to the invention and complexdevices can be produced or grown in situ. Prior to growth, preparationsof the substrates known to the person skilled in the art in this fieldcan grow devices having contact pads, sawing markers, lateralsuperconductive structures, and structured topological thin films. Allprior-art problems in the production, in particular of topologicalJosephson contacts, in the clean room are thus circumvented. This isparticularly advantageous in the case of topological materials, sincethe surface and thus the topological properties can be altered or evendestroyed by an exchange with the environment, for example, withatmospheric oxygen.

In particular, the methods according to the invention are advantageouslyassociated with high scalability at low cost and with little timeexpenditure. In contrast to conventional methods for producing nanowirequbits from the prior art, not every nanowire or nanostructure needs tobe positioned and contacted manually in the methods according to theinvention, but structured Majorana material can be deposited on asuitably prepared substrate and defined in a targeted and selectivemanner. With regard to scalability, the methods according to theinvention offer advantages as soon as the size and complexity of thedesired devices, such as qubits or quantum registers, increases.

As suitable methods for applying layers for the methods according to theinvention are to be mentioned in this case chemical vapor deposition atlow pressure (liquid-phase chemical vapor deposition, LP-CVD) andmolecular beam epitaxy (MBE) in addition to physical vapor deposition(PVD).

Chemical vapor deposition is particularly suitable for the generation offlat silicon-containing layers for the deposition of the first andsecond as well as the third and fourth additional layers in accordancewith method steps I.A, I.B, II.E and II.F.

Molecular beam epitaxy is particularly suitable for applying thefunctional layers in accordance with method steps I to K.

Epitaxial growth is understood in particular to mean that a furthercrystalline layer is deposited on a crystalline layer or on acrystalline substrate, wherein at least one crystallographic orientationof the growing crystal layer corresponds to an orientation of thecrystalline layer or of the crystalline substrate.

In addition to the in-situ production of the preferably epitaxialcontacts, the formation of a protective passivation layer, whichprotects the topological insulator (structured Majorana material) fromcontamination or chemical restructuring of the surface, is realized insitu. The topological material is effectively protected from anyexchange with atmospheric oxygen or other constituents of the naturalenvironment.

As a passivation layer, an aluminum layer 2 nm, maximally 3 nm thickcan, for example, be grown on the topological insulator, which aluminumlayer oxidizes completely after outward transfer of the sample from theinert atmosphere and, where applicable, from the ultrahigh vacuum, andthus protects the surface states of the structured Majorana materialthereunder. Furthermore, already inert metal oxide compounds, such asAl_(x)O_(y), Nb_(x)O_(y), Ti_(x)O_(y), where 0≤x, y≤1, are also suitableand inert metal compounds with other group VI elements, such as sulfur,tellurium or selenium, can also be used. Layers of pure tellurium orselenium have also proved themselves as a temporary protection of thetopological surface states.

A method according to the invention, illustrated here by way of examplewith reference to the production of a Josephson contact usingtopologically induced superconductivity, advantageously enables an inparticular epitaxial production of the in-situ contacts, which leads toa particularly high quality of the interface. In the realization ofsuperconductor/normal conductor interfaces, the quality of the interfaceis indicated by the transparency. Transparency is generally understoodto mean the probability of the successful exchange of paired electronstates via the interface, also known as Andreev reflection. The Andreevreflection process at the interface is opposite to the directbackscattering of the individual electrons at the interface. Theprobabilities of the Andreev reflection and of the normal reflection addup to 100%.

Within the framework of this invention, a method is presented forproducing a topological Josephson contact, as an example of a hybridstructure according to the invention, while maintaining the surfaceproperties of the topological material for current transport between thestructured superconductive contacts, in which method the interfacesbetween the superconductors and the structured Majorana material as atopological insulator also have a particular quality and are formed soaccurately and cleanly that Majorana physics is advantageously alsopracticable therewith. In particular, with such a hybrid structure, atopological qubit, in which, in contrast to conventional qubits,theoretically no error correction is required, can be produced.

The production of hybrid structures according to the invention,including the structured definition of the deposited Majorana material,of the structured superconductive contacts grown in situ and preferablyepitaxially, and of the passivation layer can advantageously be carriedout without interrupting the inert atmosphere, in particular in theultrahigh vacuum, within a clean room system, for example, with the aidof a molecular beam epitaxy system.

The topological material, the in-situ and preferably epitaxially grownsuperconductive contacts and the passivation layer can be deposited in amethod according to the invention in a very defined manner in a largeregion of lateral dimensions of 5 nm to 10 000 μm.

In addition, in methods according to the invention, the structures arealigned relatively to one another with deviations in the range of 2.5 nmto at most 20 nm given by the structure definition with electron beamlithography. With this method, preferably any 2D layouts of insulating,passivating and (super)conductive regions can be defined in situ.

In order to produce the structured Majorana material, the invention inparticular provides the use of a further mask (2, 3), via which thegeometry of, for example, a topological thin film can be defined, inaddition to a shadow mask.

For this purpose, the property of the topological materials of growingselectively is advantageously used. By way of example, when usingsilicon substrates, an additional layer can be applied to the substrate,on which layer the topological material does not grow at all or onlygrows when different growth parameters are selected. If the substrate isexposed in places, the topological material will deposit only in thesedefined regions. Depending on the selection of the growth parameters,the Majorana material will then grow selectively in the exposedsubregions of the silicon substrate with respect to the additionallayer.

Molecular beam epitaxy is advantageously suitable for applying thestructured superconductive layers as well as the structured Majoranamaterial, since the directed atomic/molecular flow of the materialsduring evaporation from the solid phase can advantageously be partiallyshadowed in methods according to the invention using the defined mask orusing the defined nanobridges.

In the coating method, different shadowings can advantageously beimplemented by varying the angle of incidence and omitting the substraterotation, even when a rigid mask is used. As a result, different regionsbeneath the mask can be grown or structured.

The methods according to the invention make it possible to grow orvapor-coat or cover an air-sensitive and/or environment-sensitivefunctional layer, for example, the surface of a topological insulator,in situ and selectively. At selected locations, a thick superconductivelayer is applied to the topological insulator, while at other selectedlocations only a thin layer is arranged, which after exposure to air canreact with the environment to form an insulating protective layer forthe topological insulator for example, when oxidizing materials areused. This advantageously ensures local contacting of the functionallayer and at the same time guarantees a passivation layer protecting theentire component.

In this application, a rotation of the substrate in the methodsaccording to the invention is understood to be a relative movementbetween the produced layer structure, including the substrate, and themask and the source of the coating, e.g. the molecular beam, such that,despite the shadowing effect of the mask and in particular of thenanobridges, all regions on the exposed substrate surface are covered bythe molecular beam. For this purpose, the molecular beam must, forexample, on the one hand impact the substrate or the mask at a certainangle not equal to 90°, and/or the substrate must on the other hand berotated under the molecular beam in the substrate plane during thecoating. Substrate rotations of 1-500 min⁻¹ are typical.

The functional layers can be applied without interrupting the inertatmosphere and preferably in the ultrahigh vacuum in, for example, themolecular beam epitaxy system. After outward transfer of the substratewith the defined structures from the inert atmosphere, oxidation of theregions of the superconductive material close to the surface takes placein the presence of atmospheric oxygen. In a first embodiment of theinvention (variant A), the formation of a passivating oxide layer takesplace for subregions having a layer thickness below the layer thicknessof the native oxide of the material in question. The formation of thispassivation layer on the surface of the topological insulator betweenthe two superconductive contacts causes the surface and thecurrent-carrying surface states of the topological material to beprotected.

The analysis of the local arrangement of individual atoms (by means ofatomic-probe tomography and transmission electron microscopy) of anyhybrid system makes it possible to differentiate the method describedhere from other methods, in particular to distinguish whether theindividual layers were applied in vacuo or in an inert atmosphere, andno oxygen traces can therefore be detected at the interfaces.

For subregions having a correspondingly thicker layer thickness, anoxidation layer, corresponding to the native oxide thickness, likewiseforms in a region close to the surface. However, in these subregionshaving a layer thickness above the native oxide thickness and above thecritical thickness for obtaining the superconductive properties, thematerial still has superconductive properties despite the oxidation ofthe uppermost layer at the interface with the topological material.

In a further embodiment of the method according to the invention,oxidizing materials are not exclusively used for forming the passivatinglayer. In this further embodiment (variant B), the superconductivecontacts are still defined by targeted shadowing of the atomic/molecularflow. After applying the superconductive contacts in a structured mannerand ensuring the quality of the junction between the superconductivematerial and the underlying structured Majorana material, a passivatinglayer can be deposited in a surface-covering manner over remaining,exposed subregions of the structured Majorana material. The materialsmentioned above can be used as a passivating layer, for example.

By the methods according to the invention, laterally grownheterostructures of superconductive materials and Majorana materials ofhigh quality and precise alignment can be produced. Various geometriesand dimensions allow the structured definition of functional devices,such as topological Josephson junctions, up to complex networks forapplications in scalable topological qubits as well as topologicalquantum registers.

The subject matter of the invention is explained in more detail belowwith reference to two exemplary embodiments and a number of figures.These examples are not to be understood as limiting.

In the exemplary embodiments, preferred embodiments of the methodsaccording to the invention for producing a Josephson contact using astructured Majorana material and a superconductive metal are mentionedfirst. The definition of the Josephson contact is not to be understoodas limiting but as the smallest unit of a topological qubit at the sametime serves as an illustration of the exemplary embodiments realizedthereafter. The letters of the process steps for producing an individualtopological Josephson contact correspond to those in FIGS. 1 to 6.

The method according to the invention comprises a plurality offunctional layers, wherein specific materials, which are not to beunderstood as limiting, are mentioned for use in the following exemplaryembodiments. The method is divided into a total of three submethods:preparing the substrate for a structured deposition of the Majoranamaterial (process step (I) “Selective area”), applying a stencil mask orshadow mask close to the surface for defined application of thesuperconductive metal (process step (II) “Stencil mask”) and the methodduring deposition within a molecular beam epitaxy system for directedapplication of the functional layers (process step (III) “Coatingmethod”).

Submethod I: “Selective Area”

I.A The first 5 nm of a 525 μm thick, boron-doped (>2000 Ωcm), 4″silicon wafer (1) with an orientation of the surface normal in the <111>direction are nominally converted under vacuum into silicon dioxide(SiO₂) (2), starting from the surface of the substrate. For thispurpose, a Tempress TS 8 horizontal furnace is used for the formation ofdry oxide. After oxidation at 820° C. with the aid of molecular oxygen,an actual layer thickness of 5.8 nm is achieved. The silicon dioxideconverted in this way has an etching rate in dilute hydrofluoric acid(1% HF) of 6 nm/min.

I.B A layer of stoichiometric silicon nitride (Si₃N₄) (3) nominally 20nm thick is applied areally and under vacuum to the converted silicondioxide layer (2). The silicon nitride is deposited in a CentrothermLPCVD system E1200 R&D furnace at 770° C. with the aid of 120 sccmammonia (NH₃) and 20 sccm dichlorosilane (DCS). An actual layerthickness of 25.6 nm is achieved. The resulting silicon nitride isetched at a rate of 0.4 nm/min in dilute hydrofluoric acid (1% HF).

I.C After application of the stoichiometric silicon nitride (3), saidlayer is structured. To this end, 120 nm AR-P 6200 resist is firstapplied, which is structured in a Vistec EBPG 5000+ electron beamlithography system. The electrons experience a 50 kV acceleratingvoltage with a 100 μA strong beam current. A step size of 5 nm and aproximity-corrected dose of 250 μC/cm² were chosen. The resist issubsequently developed at 0° C. for 60 seconds in AR 600-546.Development is brought to a stop in a 60-second 2-propanol bath. Afterdevelopment of the resist, the structures defined in the resist aretransferred into the stoichiometric silicon nitride (3) by means of anOxford Plasmalab 100 system. The plasma used is ignited from fluoroform(CHF₃) and molecular oxygen (O₂) in a ratio of 22 sccm CHF₃ to 2 sccm O₂at a selected power of 50 W RF power. The etching time is 90 seconds.

In the exemplary method for structuring the stoichiometric siliconnitride (3), thin trenches having a width of 40-10 000 nm are defined.The length of the trenches produced varies from 3 μm to 100 μm.

I.D The exposed subregions of the first silicon dioxide layer (2) areetched isotropically in dilute hydrofluoric acid (1% HF) for 75 seconds.The etching process is stopped in deionized water. The isotropic etchingbehavior of the silicon dioxide in the dilute hydrofluoric acid forms anetching profile close to that shown in FIG. 1, process step D.

Submethod II: “Stencil Mask”

II.E In a first step, a layer of silicon dioxide nominally 400 nm thick(4) is deposited areally and under vacuum on the structures produced insubmethod I. This layer is deposited in a Centrotherm LPCVD system E1200R&D furnace at 650° C. and with the aid of tetraethoxysilane.

Said silicon dioxide layer (4) forms the lower silicon dioxide (2) andsilicon nitride layers (3) and fills them. The upper silicon dioxidelayer (4) is chemical-mechanically polished (chemical-mechanicalplanarization, CMP) and thus smoothed.

II.F To the second silicon dioxide layer (4), a further layer ofstoichiometric silicon nitride (5) is applied areally and under vacuum.The LP-CVD process as mentioned in process step I.C is again carriedout. A layer of stoichiometric silicon nitride nominally 100 nm thick isapplied.

II.G The second layer of stoichiometric silicon nitride (5) is partiallyremoved selectively with respect to the second layer of silicon dioxide(4). The electron beam lithography process as mentioned in sub-processI.C is again carried out. Junctions are defined which ultimatelyrepresent the weak link of a simple Josephson contact. This narrowregion was already referred to as a nanobridge in the precedingcontinuous text. The junctions therefore have at least the width of thestructures previously produced in process step I.C in the first layer ofstoichiometric silicon nitride (3) and a lateral distance from eachother of 20-200 nm. The alignment of the nanobridges relative to thetrenches is carried out via corresponding markers.

III.H The second layer of silicon dioxide (4) is removed selectivelywith respect to both the silicon substrate (1) and the first layer ofsilicon dioxide (2) as well as the first (3) and second layers ofstoichiometric silicon nitride (5). In the process, the regions exposedin step II.G are removed. Viewed relatively, the etching selectivityresults from the different etching rates of the layers mentioned. It isnecessary for the method according to the invention that the secondlayer of silicon dioxide (4) be removed isotropically in all directions.As a result, any material of the second layer, comprising stoichiometricsilicon oxide (4), that is beneath the nanobridges defined in step II.Gis removed. In addition, the structures defined in submethod I arepartially exposed. The nanobridges are partially freely suspended abovethe silicon substrate (1) from this point in time onwards.

Submethod III: “Coating Method” Variant A

III.I The sample with the nanobridges and the partially exposed areas ofthe silicon substrate (1) is transferred into a molecular beam epitaxysystem for deposition of the functional layers/structures. An ultrahighvacuum of p≤1×10⁻⁹ hPa (e.g., 5×10⁻¹⁰ hPa) is set. A topologicalinsulator (6) of composition (Bi_(0.06)Sb_(0.94))₂Te₃ is deposited andgrows selectively on the exposed substrate surface. The substraterotation of 10 revolutions per minute guarantees that the aforementionedtopological insulator also grows on the exposed subregions beneath thenanobridges.

III.J A thin layer of titanium nominally 2 nm thick (7) which is capableof forming a dense native oxidation layer is applied with substraterotation in a surface-covering manner in the same molecular beam epitaxysystem. Due to the substrate rotation, this layer is also depositedbeneath the nanobridges. In the embodiment described here, the layerthickness of the titanium layer does not exceed the thickness of thenative oxide of titanium and in subsequent steps, when outwardlytransferred from the system, forms a passivation layer for thetopological insulator in subregions.

III.K A further layer of 70 nm aluminum (8) is applied without substraterotation to subregions of the previously deposited titanium layer (7).The nanobridges defined in the second layer (5) partially shadow theatomic/molecular flow.

In the present exemplary embodiment, selecting titanium as the secondfunctional layer (7) proved to be advantageous since it can serve as aninterdiffusion barrier between the first functional layer (6) and thethird functional layer (8), but selecting a different superconductivemetal, such as aluminum or niobium, as the third functional layer (8)since these metals have particularly advantageous superconductiveproperties with respect to titanium.

Submethod III: “Coating Method” Variant B

III.I The sample with the nanobridges and the partially exposed areas ofthe silicon substrate (1) is transferred into the ultrahigh vacuum(system-specifically, p≤1×10⁻⁹ hPa) of a molecular beam epitaxy systemfor deposition of the functional layers/structures. A Majorana materialcomprising (Bi_(0.06)Sb_(0.94))₂Te₃ is deposited and grows selectivelyon the exposed substrate surface. The substrate rotation of 10 min⁻¹guarantees that the Majorana material also grows on the exposedsubregions beneath the nanobridges.

After transfer within a so-called vacuum box (specifically, p≤1×10⁻⁸hPa), the sample is transferred into a molecular beam epitaxy system fordeposition of a layer of niobium nominally 70 nm thick (9). The layer isapplied without substrate rotation to subregions of the secondfunctional layer. The nanobridges defined in the second layer ofstoichiometric silicon nitride (5) partially shadow the atomic/molecularflow.

The sample is transferred into an adjacent molecular beam epitaxy systemwithout interrupting the vacuum. The layers (6) and (9) are thus heldcontinuously in an inert atmosphere until the dielectric layer (10) isapplied. A layer of stoichiometric AI₂O₃ 10 nm thick (10) is appliedareally to the entire surface of the sample. The aluminum oxide isremoved from a target of stoichiometric AI₂O₃. This layer serves toprotect the surface and the surface states of the topological insulatorbetween the subregions produced in process step III. J′ andadvantageously protects the Nb from oxidation.

In FIGS. 5 and 6, the method steps for producing, after outwardtransfer, a Josephson contact for variants A and B are shown in additionto the illustrated method. In this case, the substrate (1) and thelayers for the masks (2, 3, 4, 5) have been omitted for the sake ofsimplicity.

In variant A (FIG. 5), the structured Majorana material (6) with asecond functional layer (7) arranged thereon and the two separatelypresent regions of the third functional layer (8), each comprising asuperconductive material, are present. Upon contact with atmosphericoxygen, not only the regions close to the surfaces of the two regions ofthe third functional layer (8), shown here as (12), but also the regionsclose to the surfaces of the exposed regions of the second functionallayer (7), marked here as (11), oxidize. Because the layer thickness ofthe second functional layer (7) was chosen to be correspondingly thin,complete oxidation of the layer and thus the desired capping for thetopological insulator (6) between the separately present regions (8) ofthe third functional layer takes place here (11), while the non-exposedregions of the first functional layer (7) which are in contact with thesecond functional layer (8) do not oxidize.

In variant B (FIG. 6), the structured Majorana material (6) is presentwith the two separately arranged regions of the second functional layer(9) and a third functional layer (10) formed thereon, each comprising asuperconductive material. In this case, upon contact with atmosphericoxygen, only the region close to the surface of the third functionallayer (10), shown here as (13), oxidizes. Since the layer thickness ofthe third functional layer (10) was chosen to be correspondingly thinoverall, complete oxidation of the layer occurs here (13). As a result,the desired capping for the topological insulator (6) is achievedbetween the separately present regions (9) of the second functionallayer. If the third functional layer (10) is an insulator, this layer(10) can be selected to have any thickness.

The hybrid structures produced according to the invention canadvantageously be built up into complex networks. These networksinclude, for example, the topological Josephson contact as the smallestsubunit but may in a further embodiment represent up to a plurality oftopological quantum bits. The method according to the inventionguarantees preservation of the surface properties of the structuredMajorana material as a topological insulator, as well as a highinterface quality between the structured Majorana material and thesuperconductor.

Further applications for the invention are shown in FIG. 7. Startingfrom method step I, in addition to a Josephson junction according to theinvention with a topological insulator in wire form (6) (=G1), othergeometries of Josephson junctions, such as a topological insulator inwire form (6) with a superconductive island (9), can also be produced(=G2), wherein the superconductive island (9) can cover the topologicalinsulator completely (variant A) or only partially (variant B). In FIG.7, the plan views after process step I are shown in the left column, thefront views after process step J′ in the middle column, and the frontviews after process step K′ in the right column.

In particular, the Josephson junctions according to variant B canadvantageously also be designed as a bi-junction and as a tri-junction,as shown in FIG. 8. In FIG. 8, the plan views after process step I areshown in the left column, the front views after process step J′ in themiddle column, and the front views after process step K′ in the rightcolumn, in each case for the geometry G2 (variant B), see FIG. 7, asbi-junction and tri-junction.

While the invention has been illustrated and described in detail in thedrawings and foregoing description, such illustration and descriptionare to be considered illustrative or exemplary and not restrictive. Itwill be understood that changes and modifications may be made by thoseof ordinary skill within the scope of the following claims. Inparticular, the present invention covers further embodiments with anycombination of features from different embodiments described above andbelow.

The terms used in the claims should be construed to have the broadestreasonable interpretation consistent with the foregoing description. Forexample, the use of the article “a” or “the” in introducing an elementshould not be interpreted as being exclusive of a plurality of elements.Likewise, the recitation of “or” should be interpreted as beinginclusive, such that the recitation of “A or B” is not exclusive of “Aand B,” unless it is clear from the context or the foregoing descriptionthat only one of A and B is intended. Further, the recitation of “atleast one of A, B and C” should be interpreted as one or more of a groupof elements consisting of A, B and C, and should not be interpreted asrequiring at least one of each of the listed elements A, B and C,regardless of whether A, B and C are related as categories or otherwise.Moreover, the recitation of “A, B and/or C” or “at least one of A, B orC” should be interpreted as including any singular entity from thelisted elements, e.g., A, any subset from the listed elements, e.g., Aand B, or the entire list of elements A, B and C.

LITERATURE CITED IN THIS APPLICATION

[1] https://arxiv.org/abs/1608.00263

-   -   “Characterizing Quantum Supremacy in Near-Term Devices,” Sergio        Boixo, Sergei V. Isakov, Vadim N. Smelyanskiy, Ryan Babbush, Nan        Ding, Zhang Jiang, John M. Martinis and Hartmut Neven,        arXiv:1608.00263v2 [quant-ph] Aug. 3, 2016.

[2]http://iopscience.iop.Org/article/10.1070/1063-7869/44/10S/S29/meta:jsessionid=7B6A386E471815BB16B2CCDF05CF2B34.c3.iops cience.cld.iop.org

-   -   “Unpaired Majorana fermions in quantum wires”, A Yu Kitaev,        Chernogolovka 2000: Mesoscopic and strongly correlated electron        systems, Usp. Fiz. Nauk (Suppl.) 171 (10).

[3] http://science.sciencemaq.org/content/336/6084/1003

-   -   “Signatures of Majorana Fermions in Hybrid        Superconductor-Semiconductor Nanowire Devices,” V. Mourik, K.        Zuo, S. M. Frolov, S. R. Plissard, E. P. A. M. Bakkers, L. P.        Kouwenhoven, www.sciencemag.org SCIENCE VOL 336 May 25, 2012,        1003.

[4] https://arxiv.org/abs/1610.04555

-   -   “Experimental Phase Diagram of a One-Dimensional Topological        Superconductor”, Jun Chen, Peng Yu, John Stenger, Moira Hocevar,        Diana Car, Sébastien R. Plissard, Erik P. A. M. Bakkers,        Tudor D. Stanescu, Sergey M. Frolov, arXiv:1610.04555v1        [cond-mat.mes-hall] for this version).

[5] http://iournals.aps.org/prl/abstract/10.1103/PhysRevLett.116.257003

-   -   “Majorana Zero Mode Detected with Spin Selective Andreev        Reflection in the Vortex of a Topological Superconductor,”        Hao-Hua Sun, Kai-Wen Zhang, Lun-Hui Hu, Chuang Li, Guan-Yong        Wang, Hai-Yang Ma, Zhu-An Xu, Chun-Lei Gao, Dan-Dan Guan, Yao-Yi        Li, Canhua Liu, Dong Qian, Yi Zhou, Liang Fu, Shao-Chun Li,        Fu-Chun Zhang, and Jin-Feng Jia, Phys. Rev. Lett. 116, 257003,        published Jun. 21, 2016

[6] http://www.nature.com/articles/ncomms10303

-   -   “4TT-periodic Josephson supercurrent in HgTe-based topological        Josephson junctions,” J. Wiedenmann, E. Bocquillon, R. S.        Deacon, S. Hartinger, O. Herrmann, T. M. Klapwijk, L. Maier, C.        Ames, C. Brune, C. Gould, A. Oiwa, K. Ishibashi, S. Tarucha, H.        Buhmann, L. W. Molenkamp, Nat. Commun. 2016, 7, 10303.

[7] http://www.sciencedirect.com/science/article/pii/S002202481630Q847

-   -   “Selective area growth of Bi₂Te₃ and Sb₂Te₃ topological        insulator thin films,” Jörn Kampmeier, Christian Weyrich, Martin        Lanius, Melissa Schall, Elmar Neumann, Gregor Mussler, Thomas        Schäpers, Detlev Grützmacher, Journal of Crystal Growth, Volume        443, Jun. 1, 2016, pages 38-42.

[8] http://www.nature.com/nmat/journal/v14/n4/abs/nmat4176.html,

-   -   “Epitaxy of semiconductor-superconductor nanowires,” P.        Krogstrup, N. L. B. Ziino, W. Chang, S. M. Albrecht, M. H.        Madsen, E. Johnson, J. Nygârd, C. M. Marcus, T. S. Jespersen,        Nature Materials, 14, 400-406 (2015) doi:10.1038/nmat4176.

[9] http://www.sciencedirect.com/science/article/pii/S01679317140Q3359

-   -   “Resistless nanofabrication by stencil lithography: a        review,” O. Vazquez-Mena, L. Gross, S. Xie, L. G. Villanueva, J.        Brugger, Microelectronic Engineering, volume 132, Jan. 25, 2015,        pages 236-254.

[10] http://www.sciencedirect.com/science/article/pii/S016793179900Q477

-   -   “Nonorganic evaporation mask for superconducting        nanodevices,” T. Hoss, C. Strunk, C. Schönenberger,        Microelectronic Engineering, volume 46, issues 1-4, May 1999, 32

The invention claimed is:
 1. A method for producing a hybrid structure,the hybrid structure including at least one structured Majorana materialand at least one structured superconductive material arranged thereon,the method comprising: producing, on a substrate, a first mask forstructured application of the Majorana material and a further mask forstructured growth of the at least one superconductive material, thefirst mask and the further mask being aligned relative to one another;and applying the Majorana material to the substrate, wherein the firstmask defines the structure of the Majorana material; and applying the atleast one structured superconductive material to the structured Majoranamaterial with the aid of the further mask, wherein the applying theMajorana material and the applying the at least one structuredsuperconductive material is performed without interruption in an inertatmosphere.
 2. The method according to claim 1, wherein the first maskand the further mask are produced according to the following steps: I.Aapplying a first additional layer to the substrate, I.B applying asecond additional layer to the first additional layer, wherein the firstadditional layer is etchable selectively with respect to the secondadditional layer and the substrate, I.C structuring a surface of thesecond additional layer in such a way that at least one subregion of thesecond additional layer is exposed, I.D removing at least one exposedregion of the first additional layer beneath the at least one exposedsubregion of the second additional layer to the substrate, whereby anundercut occurs, II.E depositing a third additional layer such that theat least one exposed region of the first additional layer and the atleast one exposed region of the second additional layer are completelyfilled and the third additional layer covers the second additionallayer, II.F applying a fourth additional layer to the third additionallayer, wherein the third additional layer is etchable selectively withrespect to the fourth additional layer, the second additional layer andthe substrate, II.G. structuring and exposing a surface of the fourthadditional layer in such a way that a junction remains between at leasttwo areas, and II.H removing regions of the third additional layerbeneath exposed areas of the fourth additional layer, apart from thesubstrate, whereby a second undercut occurs, wherein the applying theMajorana material to the substrate comprises subsequently depositing theMajorana material on the substrate in a structured manner such that itis arranged within the at least one exposed region of the firstadditional layer and the at least one exposed region of the secondadditional layer.
 3. The method according to claim 2, further comprisingapplying a functional layer to the structured Majorana material and atleast partially to the exposed surface of the fourth additional layer.4. The method according to claim 2, wherein, in step II.G., the surfaceof the fourth additional layer is structured and exposed in such a waythat at least one trench having a length between 100 nm and 100 μm and awidth between 10 nm and 10 μm is produced.
 5. The method according toclaim 2, wherein the first additional layer is applied with an overalllayer thickness of between 1 nm and 20 nm.
 6. The method according toclaim 2, wherein the second additional layer is applied with an overalllayer thickness of between 5 and 250 nm.
 7. The method according toclaim 2, wherein the first additional layer and the second additionallayer are deposited with an overall layer thickness of between 15 and 50nm.
 8. The method according to claim 2, wherein the third additionallayer is applied with an overall layer thickness of between 5 and 500nm, preferably in the range of 10 to 150 nm.
 9. The method according toclaim 1, wherein the structured Majorana material includes Diracmaterials.
 10. The method according to claim 9, wherein the structuredMajorana material includes Bi_(x)Sb_(1-x))₂(Te_(y)Se_(1-y))₃, where0≤x≤1 and 0≤y≤1.
 11. The method according to claim 1, further comprisingapplying a material capable of forming a native oxidation layer to thestructured Majorana material in a surface-covering manner with a layerthickness of between 1 and 3 nm, the structured Majorana materialforming at least part of a first functional layer and the materialcapable of forming a native oxidation layer forming at least part of asecond functional layer, and wherein a third functional layer comprisingsuperconductive material is applied to subregions of the secondfunctional layer without substrate rotation.
 12. The method according toclaim 11, wherein the second functional layer includes Al_(x)O_(y),Nb_(x)O_(y), Ti_(x)O_(y), where 0≤x, y≤1.
 13. The method according toclaim 11, wherein a further superconductive material is applied as thesecond functional layer.
 14. The method according to claim 1, whereinthe structured Majorana material forms at least part of a firstfunctional layer, the method further comprising applying a secondfunctional layer comprising a further superconductive material tosubregions of the structured Majorana material without substraterotation, and applying a third functional layer comprising anelectrically insulating material to the second functional layer and afree surface of the first functional layer in a surface-covering manner.15. The method according to claim 14, in the third functional layerincludes at least an additional superconductive material.